The light-by-light contribution to the muon anomalous magnetic moment from the axial-vector mesons exchanges within the nonlocal quark model

The contribution of axial-vector mesons to the muon's anomalous magnetic moment through a light-by-light process is considered within a nonlocal quark model. The model is based on a four-quark interaction with scalar--pseudoscalar and vector--axial-vector sectors. While the transverse component of the axial-vector corresponds to a spin-1 particle, the unphysical longitudinal component is mixed with a pseudoscalar meson. The model parameters are re-fitted to the pion properties in the presence of pi-a_1 mixing. The obtained estimation for the light-by-light contribution of a_1+f_1 mesons is (3.6+-1.8)*10^{-11}.Comment: 18 pages, 10 figures, final version accepted for publication in Physical Review

\delta-derivations of n-ary algebras

We defined \delta-derivations of n-ary algebras. We described \delta-derivations of (n+1)-dimensional n-ary Filippov algebras and simple finite-dimensional Filippov algebras over algebraically closed field zero characteristic, and simple ternary Malcev algebra M_8. We constructed new examples of non-trivial \delta-derivations of Filippov algebras and new examples of non-trivial antiderivations of simple Filippov algebras.Comment: 12 page

The anomalous magnetic moment of the muon in the Standard Model

194 pages, 103 figures, bib files for the citation references are available from: https://muon-gm2-theory.illinois.eduWe review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $\alpha$ and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $\mathcal{O}(\alpha^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_\mu/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $\mathcal{O}(\alpha^2)$ and is due to hadronic vacuum polarization, whereas at $\mathcal{O}(\alpha^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_\mu^\text{SM}=116\,591\,810(43)\times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$\sigma$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics

LIDAR COMBINED SCANNING UNIT

Subject of Research. The results of lidar combined scanning unit development for locating leaks of hydrocarbons are presented The unit enables to perform high-speed scanning of the investigated space in wide and narrow angle fields. Method. Scanning in a wide angular field is produced by one-line scanning path by means of the movable aluminum mirror with a frequency of 20Hz and amplitude of 20 degrees of swing. Narrowband scanning is performed along a spiral path by the deflector. The deflection of the beam is done by rotation of the optical wedges forming part of the deflector at an angle of ±50. The control function of the scanning node is performed by a specialized software product written in C# programming language. Main Results. This scanning unit allows scanning the investigated area at a distance of 50-100 m with spatial resolution at the level of 3 cm. The positioning accuracy of the laser beam in space is 15'. The developed scanning unit gives the possibility to browse the entire investigated area for the time not more than 1 ms at a rotation frequency of each wedge from 50 to 200 Hz. The problem of unambiguous definition of the beam geographical coordinates in space is solved at the software level according to the rotation angles of the mirrors and optical wedges. Lidar system coordinates are determined by means of GPS. Practical Relevance. Development results open the possibility for increasing the spatial resolution of scanning systems of a wide range of lidars and can provide high positioning accuracy of the laser beam in space